Least Common Multiple (LCM) of 69 and 168
The least common multiple (LCM) of 69 and 168 is 3864.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 69 and 168?
First, calculate the GCD of 69 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 168 = 0 remainder 69 |
| 2 | 168 ÷ 69 = 2 remainder 30 |
| 3 | 69 ÷ 30 = 2 remainder 9 |
| 4 | 30 ÷ 9 = 3 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 67 | 12529 |
| 19 and 39 | 741 |
| 77 and 72 | 5544 |
| 30 and 54 | 270 |
| 85 and 178 | 15130 |